Prerequisites

The calculations were made in R using R-Studio. The structure of the code is essentially based on the structure of the text. The raw code is in the file order_of_code.R. The file extended with Markdown is order_of_code-doc.RMD and the file order_of_code-doc.pdf is generated from it.

The code makes extensive use of the function source to call external code. Thus, the main part of the code remains slim, well structured and readable.

Note: The base path for rmd files is the folder in which they are located, not the r-project. Consequently, order_of_code.R and order_of_code-doc.RMD are both located in the root folder of the project.

Install required packages, set some options and link the sources for the helper functions.

Remark: The current version of osmplotr has to be installed from github using devtools::install_github ("ropensci/osmplotr").

require(pacman) || install.packages("pacman")
## Loading required package: pacman
## [1] TRUE
pacman::p_load(dplyr, fitdistrplus, flexsurv, ggplot2, gridExtra, kableExtra,
               mortAAR, nlme, osmplotr, reshape2, rgdal, HMDHFDplus, Metrics,
               svMisc, tibble, tidyr, cowplot, MortalityLaws, rio,
               coda, rjags, runjags, demogR, sf, rnaturalearth, readxl,
               ggrepel)
## Installing package into '/Volumes/SanDisk/Nils/Library/R/arm64/4.3/library'
## (as 'lib' is unspecified)
## Warning: package 'osmplotr' is not available for this version of R
## 
## A version of this package for your version of R might be available elsewhere,
## see the ideas at
## https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages
## Warning: 'BiocManager' not available.  Could not check Bioconductor.
## 
## Please use `install.packages('BiocManager')` and then retry.
## Warning in p_install(package, character.only = TRUE, ...):
## Warning in library(package, lib.loc = lib.loc, character.only = TRUE,
## logical.return = TRUE, : there is no package called 'osmplotr'
## Warning in pacman::p_load(dplyr, fitdistrplus, flexsurv, ggplot2, gridExtra, : Failed to install/load:
## osmplotr
options(scipen = 999)
options(dplyr.summarise.inform = FALSE)

source("./functions/bayes_cat_poisson.R")
source("./functions/gomp_MLE.R")
source("./functions/gomp_MLE_adapted.R")
source("./functions/gomp_MLE_interval.R")
source("./functions/gomp_anthr_age.R")
source("./functions/gomp_anthr_age_r.R")
source("./functions/gomp_bayes_known_age.R")
source("./functions/gomp_known_age_r.R")
source("./functions/helper_functions.R")
source("./functions/lt_MC.R")
source("./functions/lt_MC_Gomp.R")
RNGkind("L'Ecuyer-CMRG") # conservative random number generator to avoid periodicity

Important for saving time: Decide to run extensive code anew (app. 6 h +). In addition, you can set the folder for preprocessed files.

runCodeNew <- FALSE
#runCodeNew <- TRUE

saveFileDir = "preprocessed_files"
if (saveFileDir %in% list.files(getwd())) 
 {}else{
    dir.create(file.path(".", saveFileDir), showWarnings = FALSE )
 }
## NULL

1 Chapter 01 Introduction

Figure 1: Exemplary life table curves generated by Gompertz functions with different \(\beta\) parameters.

source("./chapter_01_introduction/gompertz_distribution.R")
## Saving 7 x 5 in image

2 Chapter 02 Materials and methods

Figure 3: Hazard curve for HMD UK data of the year 1841.

source("./chapter_02_materials_and_methods/hazard_curve.R")
## Saving 7 x 5 in image

3 Chapter 03 Data

Figure 4: Major cemeteries in Greater London 1100–1850 used in the present study.

source("./chapter_03_data/London_places.R") 
## Data (c) OpenStreetMap contributors, ODbL 1.0. https://www.openstreetmap.org/copyright
## Saving 7 x 5 in image

Table 1: Overview of included cemeteries with osteoarchaeological data.

read.table("chapter_03_data/london_cemeteries.txt", header = T, sep = "\t") %>%
  knitr::kable(., caption = "Overview of included cemeteries with osteoarchaeological data.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position") %>% unclass() %>% cat()
Overview of included cemeteries with osteoarchaeological data.
Map.nr. name period excavation.date social.character absolute.n n.analysed n….12.years references
6 Bermondsey Abbey 1089–1538 1984–1995 monks 208 201 201 Dyson et al. (2011)
8 St. Mary Spital 1120–1538 1991–2007 commoners 10,516 5,387 Connell et al. (2012)
NA period 14: 1120–1200 347 329
NA period 15: 1200–1250 510 470
NA period 16: 1250–1400 1,392 1,361
NA period 17: 1400–1539 526 467
3 St. Mary Graces 1350–1540 1986–1988 commoners 378 298 Grainger/Phillpotts (2011)
7 New Churchyard 1569–1739 2011–2015 low status 3,354 682 (category A) 556 Hartle et al. (2017)
4 St. Benet Sherehog 1670–1740 1994–1996 higher status 230 179 Miles et al. (2008a)
1 St. Marylebone 1767–1859 1992; 2003 high status 301 226 Miles et al. (2008b)
2 St. Marylebone Paddington Street north 1772–1853 2012–2013 high status 385 291 232 Henderson et al. (2015)
9 Chelsea Old church 1712–1842 2000 mixed 198 168 Cowie et al. (2008)
5 St. Brides crypt 1740–1853 high 216 Scheuer, J. L. (1995); Scheuer, L. (1998)
10 St. Brides lower churchyard 1770–1849 low 606 379 Kausmally (2008)
11 St Mary and St Michaels burial ground 1843–1854 2004–2005 low, Irish immigrants 760 705 284 Henderson et al. (2013)
12 Sheens burial ground 1763–1853 2006–2007 low 265 254 172 Henderson et al. (2013)
13 Bow Baptist church 1816–1853 2006; 2008 villagers 440 416 231 Henderson et al. (2013)

Figure 5: Population development of London, compiled from Finlay/Shearer (1986), 39 table 1; Landers (1993), 41; 179 table 5.7; Weinreb et al. (2008), 655–657.

source("./chapter_03_data/London_population.R")
grid::grid.newpage()
grid::grid.draw(rbind(london_pop1, london_pop2))

Footnote 6: Re-calculation of population increase rates of London from Razzell/Spence (2007). Calculated in ./chapter_03_data/London_population.R

knitr::kable(razz_df, caption = "Re-calculation of population increase rates of London from Razzell/Spence 2007.")%>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Re-calculation of population increase rates of London from Razzell/Spence 2007.
date population rate.per.year
1520 55000 NA
1600 200000 0.016
1650 400000 0.014
1700 575000 0.007
1750 675000 0.003
1801 960000 0.007
1851 2685000 0.021

4 Chapter 04 Results

Preprocessing of data used in figure 6: Estimated modal ages.

4.1 Historical life tables

4.1.1 Written sources

Basic statistics

The data is referenced and aggregated in “./chapter_04_results/historical_lifetables.R”. In this file, all records from individual preprocessing files located in “./liftables_preprocessed/” are sourced. The corresponding data files are stored in “./data/”.

English_Peers.R, russell.txt, Source: La Poutré/Janssen (2021), table 2

source("./chapter_04_results/historical_lifetables.R")
kable(peers_ranges, caption = "English Peers") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
English Peers
parameter modes HDI.ranges
beta 0.0613 0.0559-0.0660
M 58.1758 56.4-59.8
e20 33.4148 NA
e25 29.4926 NA

Medieval_England.R, Christ_church_monks.txt, Source: Hatcher et al. (2006), 28 table 2

kable(monks_ranges, caption = "Christ Church monks") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Christ Church monks
parameter modes HDI.ranges
beta 0.0461 0.0398-0.0523
M 52.7659 48.9-56.0
e20 31.0948 NA
e25 27.7530 NA

London_1728_1840.R, Mortality_bills_1728_1840.txt, Source: Roberts/Cox (2003), 304 Table 6.5; > 100 years and < 1 year collapsed

kable(london_1728_1840_ranges, 
      caption = "London Mortality bills 1728-1840.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
London Mortality bills 1728-1840.
parameter ranges
beta 0.0326-0.0418
M 43.3-54.8
kable(london_1728_1840_ranges_r, 
      caption = "London Mortality bills 1728-1840, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
London Mortality bills 1728-1840, corrected for population growth.
parameter ranges
beta_r 0.034-0.0507
M_r 46-64.3
r 0.002-0.019

London_1841_raw_all.R, London_1841_raw.txt, Source: Graham (1842), 19 table q.

kable(London_1841_ranges, 
      caption = "Census data for London from 1841.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Census data for London from 1841.
parameter modes HDI.ranges
beta 0.0547 0.0510-0.0585
M 60.4164 58.9-61.7

English_Mortality.R, wrigley_et_al_1997_england_1640-1809.txt, Source: Wrigley et al. (1997), 290 table 6.19

kable(eng_mort_ranges, 
      caption = "English mortality data.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
English mortality data.
parameter ranges
beta 0.0438-0.0608
M 52.2-67.4

HMD_UK_ranges.R

The data from the Human Mortality Database (https://mortality.org/) were retrieved with a personal account using the R package HMDHFDplus. Therefore, we only provide the processed data here.

kable(HMD_UK_ranges, caption = "Human Mortality Database UK.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Human Mortality Database UK.
parameter ranges
beta 0.05-0.0654
M 64.2-70.2

Extended statistics

kable(peers_result, caption = "English Peers.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
English Peers.
PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
a 1.000356 1.001061 0.0044095 0.0043879 0.0043263 11315.3 0.0000044 0.95 0.0035238 0.0053575
b 1.000307 1.000854 0.0609452 0.0609518 0.0612976 11121.9 0.0000244 0.95 0.0559415 0.0660412
M 1.000196 1.000696 58.1500750 58.1648975 58.1757927 20660.4 0.0059675 0.95 56.4492001 59.8036275
kable(monks_result, caption = "Christ Church monks.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Christ Church monks.
start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
1395 1505 alpha 1.000569 1.001661 0.0102993 0.0102563 0.0100488 13991.9 0.0000096 0.95 0.0081076 0.0125497
1395 1505 beta 1.000498 1.001436 0.0459467 0.0459287 0.0461060 13623.6 0.0000273 0.95 0.0397953 0.0523389
1395 1505 M 1.000504 1.001504 52.5281106 52.6296486 52.7658924 15808.5 0.0143226 0.95 48.9344189 55.9631681
kable(london_1728_1840_result, 
      caption = "London Mortality bills 1728-1840.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London Mortality bills 1728-1840.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1728 alpha 1.000087 1.000306 0.0146842 0.0146345 0.0145833 17556.5 0.0000101 0.95 0.0121424 0.0173529
X1728 beta 1.000115 1.000412 0.0349280 0.0349276 0.0347502 17418.0 0.0000202 0.95 0.0296810 0.0401486
X1728 M 1.000083 1.000299 44.6441200 44.8860914 45.5314756 17327.3 0.0224261 0.95 38.6469401 50.0270569
X1730 alpha 1.000130 1.000390 0.0156561 0.0155984 0.0155550 17707.3 0.0000113 0.95 0.0127651 0.0186532
X1730 beta 1.000044 1.000181 0.0325647 0.0325599 0.0325660 17242.0 0.0000212 0.95 0.0271489 0.0380817
X1730 M 1.000124 1.000377 42.2325103 42.5795321 43.3073366 17007.1 0.0285150 0.95 34.7635858 49.1029390
X1740 alpha 1.000404 1.001423 0.0153988 0.0153491 0.0151995 17959.5 0.0000100 0.95 0.0128421 0.0180871
X1740 beta 1.000376 1.001376 0.0337368 0.0337428 0.0337806 17712.7 0.0000192 0.95 0.0286838 0.0387413
X1740 M 1.000496 1.001609 43.0631632 43.3280277 43.9606200 17454.0 0.0235235 0.95 36.6700553 48.6880952
X1750 alpha 1.000135 1.000198 0.0151763 0.0151270 0.0150364 18259.1 0.0000101 0.95 0.0125377 0.0178563
X1750 beta 1.000114 1.000178 0.0342964 0.0342869 0.0341703 18177.8 0.0000196 0.95 0.0290894 0.0394288
X1750 M 1.000179 1.000275 43.5924225 43.8460270 44.4983607 17767.1 0.0230817 0.95 37.4073951 49.2703888
X1760 alpha 1.000177 1.000629 0.0145817 0.0145330 0.0143877 17316.9 0.0000100 0.95 0.0120971 0.0172323
X1760 beta 1.000136 1.000506 0.0350143 0.0350086 0.0350484 17001.2 0.0000202 0.95 0.0298241 0.0401131
X1760 M 1.000187 1.000641 44.8612069 45.0945299 45.4484334 17136.0 0.0220610 0.95 39.0545641 50.2289914
X1770 alpha 1.000210 1.000234 0.0143004 0.0142472 0.0140950 17376.2 0.0000100 0.95 0.0117447 0.0168976
X1770 beta 1.000111 1.000112 0.0356448 0.0356520 0.0357779 17075.8 0.0000206 0.95 0.0303640 0.0408917
X1770 M 1.000272 1.000317 45.4735868 45.7082853 46.2765443 17338.6 0.0215703 0.95 39.8841834 50.8485089
X1780 alpha 1.000514 1.001561 0.0136096 0.0135643 0.0135416 17117.8 0.0000093 0.95 0.0112683 0.0160201
X1780 beta 1.000465 1.001440 0.0367597 0.0367653 0.0367765 16987.0 0.0000198 0.95 0.0317257 0.0418630
X1780 M 1.000566 1.001711 46.9184820 47.1022825 47.2254317 17138.4 0.0191612 0.95 41.9217381 51.6370888
X1790 alpha 1.001017 1.003544 0.0126577 0.0126131 0.0125275 16575.3 0.0000091 0.95 0.0104144 0.0149800
X1790 beta 1.000983 1.003179 0.0385025 0.0385094 0.0386019 16305.1 0.0000206 0.95 0.0333766 0.0437012
X1790 M 1.000966 1.003389 48.8104699 48.9690668 49.1799758 17098.7 0.0174550 0.95 44.3144300 53.1380827
X1800 alpha 1.000110 1.000420 0.0116860 0.0116468 0.0115927 16299.7 0.0000084 0.95 0.0096049 0.0137829
X1800 beta 1.000087 1.000347 0.0399538 0.0399387 0.0396845 16015.0 0.0000202 0.95 0.0349411 0.0449695
X1800 M 1.000108 1.000414 50.7157959 50.8389930 51.1834695 17252.3 0.0153333 0.95 46.6384629 54.4728117
X1810 alpha 1.000243 1.000527 0.0115193 0.0114800 0.0114383 15734.5 0.0000082 0.95 0.0095164 0.0135694
X1810 beta 1.000118 1.000358 0.0383935 0.0383896 0.0384657 15460.0 0.0000197 0.95 0.0335364 0.0431518
X1810 M 1.000326 1.000622 51.2962821 51.4292427 51.6215562 16508.4 0.0161901 0.95 47.0977231 55.2320786
X1820 alpha 1.000052 1.000181 0.0104841 0.0104445 0.0102781 15011.2 0.0000079 0.95 0.0086351 0.0124260
X1820 beta 1.000027 1.000124 0.0403826 0.0403829 0.0404617 14970.0 0.0000204 0.95 0.0354909 0.0452688
X1820 M 1.000055 1.000187 53.3587767 53.4706305 53.7399168 16366.7 0.0145839 0.95 49.6763807 56.9584942
X1830 alpha 1.000258 1.000430 0.0098584 0.0098256 0.0097258 14395.4 0.0000077 0.95 0.0080812 0.0116651
X1830 beta 1.000286 1.000581 0.0420293 0.0420238 0.0418237 14224.9 0.0000211 0.95 0.0371298 0.0469784
X1830 M 1.000236 1.000371 54.4809550 54.5648372 54.7531694 16267.7 0.0133487 0.95 51.0810043 57.7147665
X1840 alpha 1.000201 1.000590 0.0103011 0.0102629 0.0101990 14208.6 0.0000081 0.95 0.0084545 0.0122232
X1840 beta 1.000209 1.000633 0.0409196 0.0409247 0.0410181 14009.2 0.0000213 0.95 0.0359043 0.0457889
X1840 M 1.000202 1.000548 53.6779375 53.7846103 53.9681394 15624.6 0.0146214 0.95 50.0085204 57.1315996
kable(london_1728_1840_result_r, 
      caption = "London Mortality bills 1728-1840, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London Mortality bills 1728-1840, corrected for population growth.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1728 alpha 1.000216 1.000632 0.0117973 0.0117320 0.0118127 12703.3 0.0000126 0.95 0.0090855 0.0145984
X1728 beta 1.000264 1.000811 0.0383802 0.0383752 0.0385662 13742.4 0.0000251 0.95 0.0326747 0.0441749
X1728 M 1.000177 1.000534 50.6676878 50.8590788 51.5853562 13177.1 0.0252464 0.95 44.7887126 56.0258710
X1728 rate 1.000032 1.000061 0.0067646 0.0067607 0.0067957 25886.2 0.0000155 0.95 0.0018885 0.0116701
X1730 alpha 1.000179 1.000607 0.0143632 0.0142738 0.0140413 13423.4 0.0000148 0.95 0.0111303 0.0178349
X1730 beta 1.000209 1.000645 0.0340807 0.0340719 0.0339992 14402.5 0.0000247 0.95 0.0282252 0.0398462
X1730 M 1.000167 1.000545 45.1548428 45.5041559 46.1942144 13398.1 0.0340936 0.95 37.2310898 52.4481763
X1730 rate 1.000100 1.000359 0.0021254 0.0021267 0.0023925 28508.1 0.0000148 0.95 -0.0027647 0.0070247
X1740 alpha 1.000250 1.000351 0.0143131 0.0142474 0.0141781 12578.6 0.0000142 0.95 0.0112583 0.0174506
X1740 beta 1.000181 1.000319 0.0351166 0.0351062 0.0349517 13779.1 0.0000232 0.95 0.0297582 0.0404467
X1740 M 1.000278 1.000415 45.4168492 45.6666273 45.9931494 12599.0 0.0307477 0.95 38.5335175 51.8684034
X1740 rate 1.000068 1.000120 0.0016517 0.0016515 0.0015142 25567.8 0.0000156 0.95 -0.0031950 0.0065573
X1750 alpha 1.000044 1.000069 0.0122439 0.0121749 0.0120834 13261.9 0.0000125 0.95 0.0094963 0.0150957
X1750 beta 1.000071 1.000205 0.0376537 0.0376479 0.0373656 14801.1 0.0000236 0.95 0.0320020 0.0432862
X1750 M 1.000031 1.000056 49.7546558 49.9590937 50.2151068 13705.5 0.0254226 0.95 43.7054776 55.2902303
X1750 rate 1.000077 1.000111 0.0067105 0.0067114 0.0065398 27317.4 0.0000151 0.95 0.0018180 0.0115565
X1760 alpha 1.000225 1.000700 0.0116585 0.0115897 0.0114879 12463.7 0.0000123 0.95 0.0090429 0.0144036
X1760 beta 1.000110 1.000420 0.0385112 0.0385024 0.0386022 13804.0 0.0000244 0.95 0.0328832 0.0441388
X1760 M 1.000236 1.000723 50.9671802 51.1574788 51.4559256 12906.8 0.0247727 0.95 45.4374663 56.3675483
X1760 rate 1.000227 1.000754 0.0069377 0.0069444 0.0071785 25388.2 0.0000156 0.95 0.0020562 0.0118077
X1770 alpha 1.000913 1.002565 0.0119572 0.0118855 0.0116788 12401.3 0.0000128 0.95 0.0092493 0.0148011
X1770 beta 1.000842 1.002526 0.0385160 0.0385119 0.0385913 13729.2 0.0000249 0.95 0.0328861 0.0442661
X1770 M 1.000933 1.002591 50.3026157 50.5009459 50.9360513 12779.1 0.0255623 0.95 44.5382288 55.7354351
X1770 rate 1.000327 1.001024 0.0054059 0.0053991 0.0053967 26694.8 0.0000153 0.95 0.0005155 0.0103390
X1780 alpha 1.000024 1.000080 0.0098947 0.0098375 0.0097623 12144.8 0.0000109 0.95 0.0076036 0.0122621
X1780 beta 1.000089 1.000332 0.0416234 0.0416156 0.0412466 13529.3 0.0000249 0.95 0.0357590 0.0470951
X1780 M 1.000009 1.000034 54.5099445 54.6330090 54.9472107 13234.3 0.0205386 0.95 49.7839622 58.9932689
X1780 rate 1.000029 1.000052 0.0101105 0.0101157 0.0102186 23262.7 0.0000163 0.95 0.0051865 0.0149529
X1790 alpha 1.000780 1.002619 0.0074628 0.0074099 0.0072730 12511.4 0.0000086 0.95 0.0056365 0.0093699
X1790 beta 1.000634 1.002266 0.0465156 0.0465133 0.0464524 13814.5 0.0000257 0.95 0.0405791 0.0524046
X1790 M 1.000594 1.002037 59.3920496 59.4676688 59.6465203 15210.4 0.0154250 0.95 55.6352570 63.0795140
X1790 rate 1.000364 1.001370 0.0165769 0.0165808 0.0166141 24083.9 0.0000160 0.95 0.0116026 0.0213767
X1800 alpha 1.000673 1.001733 0.0067061 0.0066571 0.0065314 12303.3 0.0000078 0.95 0.0050738 0.0084373
X1800 beta 1.000450 1.001205 0.0482926 0.0482882 0.0482750 13472.8 0.0000254 0.95 0.0425605 0.0540970
X1800 M 1.000481 1.001391 60.9494935 61.0079704 61.2925933 16004.8 0.0138784 0.95 57.4654475 64.3420718
X1800 rate 1.000147 1.000554 0.0172842 0.0172863 0.0173351 24114.8 0.0000161 0.95 0.0123533 0.0221326
X1810 alpha 1.000778 1.002825 0.0061205 0.0060764 0.0060231 11885.0 0.0000073 0.95 0.0046308 0.0077169
X1810 beta 1.000722 1.002651 0.0477278 0.0477231 0.0477969 12935.3 0.0000252 0.95 0.0421088 0.0533294
X1810 M 1.000533 1.001967 63.1111594 63.1645788 63.3883652 15759.0 0.0139295 0.95 59.6818113 66.5370162
X1810 rate 1.000355 1.001232 0.0188379 0.0188404 0.0189439 21465.1 0.0000169 0.95 0.0139210 0.0236200
X1820 alpha 1.000095 1.000132 0.0055976 0.0055572 0.0054458 11229.6 0.0000070 0.95 0.0041772 0.0070725
X1820 beta 1.000042 1.000144 0.0497736 0.0497549 0.0494675 11848.9 0.0000269 0.95 0.0440723 0.0555463
X1820 M 1.000089 1.000100 63.9900524 64.0294417 64.0859524 15792.1 0.0130000 0.95 60.7385660 67.1324448
X1820 rate 1.000054 1.000169 0.0184286 0.0184243 0.0183352 20638.3 0.0000173 0.95 0.0136164 0.0233407
X1830 alpha 1.000685 1.002323 0.0055328 0.0054915 0.0053316 10784.7 0.0000071 0.95 0.0041241 0.0069785
X1830 beta 1.000541 1.001972 0.0507604 0.0507524 0.0506613 11479.7 0.0000273 0.95 0.0450068 0.0564989
X1830 M 1.000452 1.001586 63.7527679 63.7940673 63.8373687 14596.3 0.0130407 0.95 60.6000558 66.7627670
X1830 rate 1.000340 1.001284 0.0170084 0.0170011 0.0170444 20042.5 0.0000176 0.95 0.0121792 0.0219144
X1840 alpha 1.000307 1.001096 0.0054664 0.0054244 0.0053739 11068.3 0.0000069 0.95 0.0040888 0.0069308
X1840 beta 1.000429 1.001483 0.0504923 0.0504880 0.0504433 12336.9 0.0000266 0.95 0.0445658 0.0561736
X1840 M 1.000118 1.000460 64.1209693 64.1581002 64.3153799 15983.6 0.0125993 0.95 61.0149913 67.2673873
X1840 rate 1.000057 1.000244 0.0185439 0.0185336 0.0183673 20908.7 0.0000172 0.95 0.0136249 0.0233586
kable(London_1841_result, 
      caption = "Census data for London from 1841.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Census data for London from 1841.
PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
a 1.000227 1.000481 0.0045780 0.0045654 0.0045126 15366.4 0.0000030 0.95 0.0038745 0.0053284
b 1.000173 1.000361 0.0547652 0.0547581 0.0546507 15261.7 0.0000155 0.95 0.0510256 0.0585294
M 1.000098 1.000288 60.3512664 60.3640713 60.4164328 26323.3 0.0044223 0.95 58.9378882 61.7484732
kable(eng_mort_result, caption = "English mortality data.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
English mortality data.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1640 alpha 1.000116 1.000213 0.0109640 0.0109440 0.0108724 20086.8 0.0000055 0.95 0.0094508 0.0125183
X1640 beta 1.000128 1.000269 0.0473794 0.0473646 0.0471615 19457.0 0.0000160 0.95 0.0430271 0.0517521
X1640 M 1.000098 1.000168 55.8790864 55.9257645 56.0762781 22766.9 0.0074788 0.95 53.6542245 58.0607633
X1650 alpha 1.000196 1.000699 0.0086495 0.0086305 0.0086386 17477.0 0.0000050 0.95 0.0073694 0.0099516
X1650 beta 1.000238 1.000818 0.0534298 0.0534191 0.0532174 17097.8 0.0000176 0.95 0.0488730 0.0579356
X1650 M 1.000122 1.000456 59.0892102 59.1180884 59.1222939 22875.6 0.0058105 0.95 57.3707403 60.8059797
X1660 alpha 1.000538 1.001899 0.0091323 0.0091133 0.0090836 17736.5 0.0000051 0.95 0.0078190 0.0104985
X1660 beta 1.000442 1.001588 0.0507107 0.0507012 0.0506517 17263.0 0.0000172 0.95 0.0463039 0.0551739
X1660 M 1.000484 1.001711 58.8100849 58.8427992 58.8427140 22595.3 0.0063824 0.95 56.9061034 60.6611103
X1670 alpha 1.000280 1.000678 0.0109726 0.0109471 0.0109033 20090.3 0.0000056 0.95 0.0094600 0.0125515
X1670 beta 1.000338 1.000812 0.0444972 0.0445019 0.0446316 19399.7 0.0000157 0.95 0.0402542 0.0488448
X1670 M 1.000211 1.000529 56.4443366 56.5061422 56.5992418 22544.4 0.0083487 0.95 53.9239107 58.8183187
X1680 alpha 1.000560 1.001531 0.0134499 0.0134251 0.0133309 22339.5 0.0000061 0.95 0.0116869 0.0152420
X1680 beta 1.000479 1.001399 0.0435646 0.0435605 0.0437501 21337.1 0.0000151 0.95 0.0392159 0.0478531
X1680 M 1.000597 1.001611 51.9412993 52.0117614 52.1884363 23152.8 0.0091727 0.95 49.1667363 54.6014009
X1690 alpha 1.000203 1.000424 0.0100036 0.0099815 0.0099278 19068.4 0.0000053 0.95 0.0085828 0.0114492
X1690 beta 1.000217 1.000487 0.0457255 0.0457144 0.0457837 18458.1 0.0000160 0.95 0.0414631 0.0499716
X1690 M 1.000156 1.000323 58.2265512 58.2748183 58.3311613 22552.3 0.0076819 0.95 55.9044003 60.4191960
X1700 alpha 1.000247 1.000813 0.0097904 0.0097696 0.0097670 19048.9 0.0000052 0.95 0.0083976 0.0112137
X1700 beta 1.000228 1.000792 0.0469162 0.0469091 0.0468449 18524.9 0.0000160 0.95 0.0426635 0.0512282
X1700 M 1.000210 1.000697 58.3940436 58.4388608 58.4010030 22362.5 0.0073779 0.95 56.2165699 60.5292073
X1710 alpha 1.000629 1.002202 0.0076344 0.0076175 0.0075883 16583.9 0.0000046 0.95 0.0064833 0.0088178
X1710 beta 1.000810 1.002798 0.0547320 0.0547184 0.0547561 16149.3 0.0000181 0.95 0.0502213 0.0592441
X1710 M 1.000354 1.001230 61.0059909 61.0278089 61.0396872 23904.2 0.0053119 0.95 59.3643989 62.5807876
X1720 alpha 1.000438 1.001584 0.0080028 0.0079824 0.0079301 17173.5 0.0000047 0.95 0.0068173 0.0092105
X1720 beta 1.000453 1.001645 0.0560063 0.0560001 0.0558861 16622.0 0.0000179 0.95 0.0514205 0.0604697
X1720 M 1.000297 1.001094 59.7548666 59.7785061 59.8227855 23615.5 0.0051845 0.95 58.1648789 61.2877274
X1730 alpha 1.000128 1.000485 0.0067962 0.0067781 0.0067500 15125.2 0.0000045 0.95 0.0057413 0.0078882
X1730 beta 1.000132 1.000481 0.0561362 0.0561233 0.0561525 14537.5 0.0000193 0.95 0.0516431 0.0607418
X1730 M 1.000086 1.000325 62.6345173 62.6558894 62.6742840 23395.6 0.0050475 0.95 61.1122439 64.1406077
X1740 alpha 1.000185 1.000678 0.0067863 0.0067674 0.0067507 15383.6 0.0000045 0.95 0.0057019 0.0078702
X1740 beta 1.000260 1.000953 0.0566936 0.0566911 0.0568096 15043.4 0.0000191 0.95 0.0520709 0.0612724
X1740 M 1.000063 1.000245 62.4655115 62.4849711 62.4345863 22893.7 0.0051037 0.95 60.9419302 63.9688404
X1750 alpha 1.000389 1.001407 0.0053793 0.0053645 0.0053635 13451.8 0.0000040 0.95 0.0044682 0.0062959
X1750 beta 1.000443 1.001627 0.0595510 0.0595305 0.0594825 12966.5 0.0000210 0.95 0.0548610 0.0642515
X1750 M 1.000167 1.000607 65.4071998 65.4213962 65.4642394 24607.7 0.0044311 0.95 64.0354191 66.7582250
X1760 alpha 1.000180 1.000387 0.0080565 0.0080378 0.0079359 17802.8 0.0000047 0.95 0.0068516 0.0092887
X1760 beta 1.000187 1.000346 0.0488550 0.0488417 0.0488743 16840.4 0.0000169 0.95 0.0445037 0.0531121
X1760 M 1.000119 1.000328 61.9016665 61.9336352 62.0050035 23618.5 0.0063598 0.95 59.9327761 63.7618010
X1770 alpha 1.000469 1.001234 0.0067654 0.0067476 0.0066997 14881.8 0.0000045 0.95 0.0057073 0.0078687
X1770 beta 1.000501 1.001341 0.0538935 0.0538804 0.0536262 14373.8 0.0000192 0.95 0.0494452 0.0584665
X1770 M 1.000270 1.000709 63.5277738 63.5489910 63.4921572 22585.6 0.0054864 0.95 61.9173469 65.1383522
X1780 alpha 1.000347 1.001235 0.0066384 0.0066225 0.0066110 15713.1 0.0000043 0.95 0.0055976 0.0076907
X1780 beta 1.000349 1.001303 0.0570824 0.0570677 0.0571475 15127.7 0.0000188 0.95 0.0526292 0.0616896
X1780 M 1.000195 1.000710 62.7166530 62.7352113 62.7235429 24154.0 0.0048243 0.95 61.2201635 64.1540268
X1790 alpha 1.000180 1.000376 0.0058127 0.0057951 0.0057825 13899.0 0.0000042 0.95 0.0048677 0.0068164
X1790 beta 1.000229 1.000478 0.0580897 0.0580826 0.0579337 13447.1 0.0000206 0.95 0.0533856 0.0627649
X1790 M 1.000055 1.000174 64.6577738 64.6756380 64.7246120 23430.8 0.0047208 0.95 63.2361972 66.0657933
X1800 alpha 1.000697 1.002167 0.0046142 0.0045977 0.0045567 12391.5 0.0000037 0.95 0.0038253 0.0054317
X1800 beta 1.000709 1.002222 0.0608363 0.0608357 0.0608310 11940.3 0.0000219 0.95 0.0561091 0.0654678
X1800 M 1.000239 1.000822 67.4325112 67.4451148 67.4486965 26907.8 0.0039816 0.95 66.1359322 68.6958522
kable(HMD_UK_result, caption = "Human Mortality Database UK.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Human Mortality Database UK.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1841 alpha 1.000163 1.000417 0.0036316 0.0036148 0.0035704 13786.9 0.0000032 0.95 0.0029186 0.0043694
X1841 beta 1.000156 1.000468 0.0519888 0.0519880 0.0522191 13557.1 0.0000185 0.95 0.0476828 0.0561015
X1841 M 1.000083 1.000148 66.2542881 66.2748935 66.3111134 25227.7 0.0056085 0.95 64.4997322 67.9878895
X1845 alpha 1.000079 1.000297 0.0042938 0.0042780 0.0042669 14758.1 0.0000036 0.95 0.0034647 0.0051540
X1845 beta 1.000067 1.000247 0.0498996 0.0498859 0.0500069 14606.7 0.0000180 0.95 0.0455985 0.0541474
X1845 M 1.000065 1.000255 64.2120906 64.2353737 64.2258466 24443.1 0.0062539 0.95 62.2412879 66.0782225
X1850 alpha 1.000973 1.003549 0.0037558 0.0037391 0.0036783 13963.2 0.0000033 0.95 0.0030110 0.0045196
X1850 beta 1.000868 1.003159 0.0517607 0.0517548 0.0515669 13902.2 0.0000185 0.95 0.0475374 0.0561228
X1850 M 1.000670 1.002447 65.7445767 65.7656894 65.8470383 24788.4 0.0057544 0.95 63.9683713 67.5152044
X1855 alpha 1.000156 1.000325 0.0034310 0.0034165 0.0034148 13071.2 0.0000031 0.95 0.0027387 0.0041407
X1855 beta 1.000111 1.000252 0.0533405 0.0533264 0.0532089 12901.9 0.0000193 0.95 0.0489858 0.0575821
X1855 M 1.000055 1.000176 66.5070750 66.5214941 66.5377049 24496.9 0.0055156 0.95 64.7810996 68.1628553
X1860 alpha 1.000103 1.000169 0.0034785 0.0034615 0.0034062 13432.3 0.0000031 0.95 0.0027794 0.0041924
X1860 beta 1.000118 1.000200 0.0532621 0.0532640 0.0532106 13350.6 0.0000189 0.95 0.0490210 0.0575846
X1860 M 1.000016 1.000032 66.2956647 66.3134949 66.3500169 24949.1 0.0054798 0.95 64.5756127 67.9675086
X1865 alpha 1.000093 1.000333 0.0035991 0.0035837 0.0035330 13810.1 0.0000031 0.95 0.0028932 0.0043267
X1865 beta 1.000108 1.000353 0.0530530 0.0530491 0.0530859 13658.1 0.0000185 0.95 0.0488013 0.0572954
X1865 M 1.000045 1.000177 65.7780212 65.7953467 65.8802464 25507.4 0.0054316 0.95 64.0717897 67.4665740
X1870 alpha 1.000077 1.000191 0.0035027 0.0034908 0.0034765 13760.3 0.0000030 0.95 0.0028292 0.0042127
X1870 beta 1.000110 1.000242 0.0536849 0.0536587 0.0535650 13616.9 0.0000184 0.95 0.0495385 0.0579499
X1870 M 1.000013 1.000070 65.9071237 65.9205478 65.8577523 25746.8 0.0052524 0.95 64.2645935 67.5678728
X1875 alpha 1.000092 1.000343 0.0030605 0.0030478 0.0030211 12815.0 0.0000028 0.95 0.0024475 0.0036823
X1875 beta 1.000131 1.000471 0.0568401 0.0568279 0.0568980 12685.7 0.0000193 0.95 0.0526071 0.0611415
X1875 M 1.000031 1.000141 66.4668857 66.4785272 66.5086127 26537.0 0.0047162 0.95 64.9506366 67.9602202
X1880 alpha 1.000119 1.000291 0.0027376 0.0027242 0.0026867 12292.1 0.0000026 0.95 0.0021904 0.0033047
X1880 beta 1.000171 1.000388 0.0580794 0.0580802 0.0580583 12275.9 0.0000195 0.95 0.0538930 0.0623071
X1880 M 1.000016 1.000046 67.6639684 67.6752899 67.6594434 26763.5 0.0045057 0.95 66.2138218 69.0997903
X1885 alpha 1.000329 1.000699 0.0024297 0.0024169 0.0023954 11472.9 0.0000024 0.95 0.0019319 0.0029532
X1885 beta 1.000279 1.000617 0.0605593 0.0605577 0.0605172 11375.3 0.0000207 0.95 0.0561612 0.0648427
X1885 M 1.000124 1.000309 68.1749533 68.1842585 68.1928238 26834.9 0.0042250 0.95 66.8018933 69.5153058
X1890 alpha 1.000121 1.000451 0.0024118 0.0023997 0.0023802 11867.7 0.0000024 0.95 0.0019247 0.0029285
X1890 beta 1.000146 1.000531 0.0614665 0.0614588 0.0613662 11669.1 0.0000205 0.95 0.0571518 0.0657954
X1890 M 1.000045 1.000148 67.7519542 67.7613179 67.8037905 28081.6 0.0040695 0.95 66.4069818 69.0759956
X1895 alpha 1.000328 1.001210 0.0019825 0.0019735 0.0019634 10586.6 0.0000021 0.95 0.0015598 0.0024219
X1895 beta 1.000267 1.000994 0.0637922 0.0637712 0.0636859 10594.5 0.0000217 0.95 0.0594245 0.0681856
X1895 M 1.000224 1.000819 69.4924393 69.4994274 69.5249671 28489.7 0.0038280 0.95 68.2103261 70.7410684
X1900 alpha 1.000051 1.000194 0.0017882 0.0017794 0.0017686 10113.1 0.0000020 0.95 0.0013975 0.0021792
X1900 beta 1.000061 1.000247 0.0653147 0.0653019 0.0653664 10036.7 0.0000222 0.95 0.0609626 0.0696771
X1900 M 1.000007 1.000020 70.1656919 70.1713832 70.1615274 28126.0 0.0036879 0.95 68.9548389 71.3801825

4.2 London cemeteries

The data is mainly hard coded in the file ./chapter_04_results/Wellcome_DB.R.

Only St. Bride’s crypt is excluded but available from the Museum of London upon request. For general information: https://www.museumoflondon.org.uk go for: Collections > Archaeology at the Museum of London > Wellcome Osteological Research Database > St. Bride’s Church Fleet Street. If runCodeNew == TRUE the file ./lifetables_processing/stbrides_crypt.R will ask for the location of the retrieved dataset (Excel sheet) and process the data. In any other case pre-processed data will be loaded.

source("./lifetables_processing/stbrides_crypt.R")
source("./chapter_04_results/Wellcome_DB.R")
kable(wellcome_result, caption = "London cemeteries data.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London cemeteries data.
cemetery start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
Bermondsey Abbey 1089 1538 alpha 1.000095 1.000352 0.0119872 0.0118695 0.0117349 26882.4 0.0000115 0.95 0.0084108 0.0157410
Bermondsey Abbey 1089 1538 beta 1.000115 1.000319 0.0410531 0.0410516 0.0413654 23098.5 0.0000312 0.95 0.0318561 0.0503895
Bermondsey Abbey 1089 1538 M 1.000071 1.000266 41.8366810 42.1437778 42.5664355 29309.6 0.0207896 0.95 34.6719658 48.4310632
St. Mary Graces 1350 1540 alpha 1.000196 1.000732 0.0197808 0.0196850 0.0195223 35662.0 0.0000118 0.95 0.0154857 0.0241619
St. Mary Graces 1350 1540 beta 1.000244 1.000894 0.0346722 0.0346636 0.0349129 29450.8 0.0000239 0.95 0.0266567 0.0427213
St. Mary Graces 1350 1540 M 1.000288 1.000951 27.6620555 28.2853721 29.0829030 31343.0 0.0275212 0.95 17.7908628 36.1544161
St. Mary Hospital, 1120-1200 1120 1200 alpha 1.000021 1.000058 0.0249328 0.0248411 0.0247596 47240.6 0.0000108 0.95 0.0203838 0.0295337
St. Mary Hospital, 1120-1200 1120 1200 beta 1.000010 1.000041 0.0363031 0.0363142 0.0366087 42155.0 0.0000184 0.95 0.0288655 0.0437148
St. Mary Hospital, 1120-1200 1120 1200 M 1.000014 1.000048 21.9000883 22.4278307 23.6171674 41316.5 0.0217592 0.95 12.9358328 29.6933479
St. Mary Hospital, 1200-1250 1200 1250 alpha 1.000142 1.000479 0.0299501 0.0298832 0.0296347 50227.8 0.0000103 0.95 0.0254561 0.0345077
St. Mary Hospital, 1200-1250 1200 1250 beta 1.000145 1.000390 0.0356927 0.0356959 0.0355017 44544.0 0.0000163 0.95 0.0288836 0.0423855
St. Mary Hospital, 1200-1250 1200 1250 M 1.000138 1.000388 16.4726206 16.9685941 17.8228768 43773.7 0.0209091 0.95 7.6941741 24.3391668
St. Mary Hospital, 1250-1400 1250 1400 alpha 1.000058 1.000230 0.0183232 0.0182986 0.0182568 30711.1 0.0000060 0.95 0.0162397 0.0203837
St. Mary Hospital, 1250-1400 1250 1400 beta 1.000039 1.000160 0.0580756 0.0580643 0.0577145 27569.9 0.0000162 0.95 0.0529190 0.0634424
St. Mary Hospital, 1250-1400 1250 1400 M 1.000056 1.000226 31.8403051 31.8802975 31.9815271 32452.4 0.0050096 0.95 30.0460798 33.5688087
St. Mary Hospital, 1400-1539 1400 1539 alpha 1.000184 1.000413 0.0262455 0.0261845 0.0258468 45106.6 0.0000098 0.95 0.0222297 0.0303974
St. Mary Hospital, 1400-1539 1400 1539 beta 1.000202 1.000384 0.0374668 0.0374646 0.0373648 37992.2 0.0000178 0.95 0.0307176 0.0443176
St. Mary Hospital, 1400-1539 1400 1539 M 1.000255 1.000509 21.1562579 21.5422484 22.2118499 38394.6 0.0188420 0.95 13.7317283 27.8355824
New Churchyard 1569 1739 alpha 1.000100 1.000375 0.0257447 0.0256826 0.0256229 40693.9 0.0000097 0.95 0.0219664 0.0296497
New Churchyard 1569 1739 beta 1.000143 1.000447 0.0365472 0.0365523 0.0364771 33659.4 0.0000185 0.95 0.0298776 0.0431955
New Churchyard 1569 1739 M 1.000167 1.000489 21.2258180 21.6422371 22.4873708 34065.6 0.0202506 0.95 13.6829257 27.9012158
St. Benet Sherehog 1670 1740 alpha 1.000103 1.000388 0.0159324 0.0158024 0.0157241 35332.7 0.0000126 0.95 0.0114989 0.0206750
St. Benet Sherehog 1670 1740 beta 1.000166 1.000541 0.0354819 0.0354675 0.0352938 29914.9 0.0000268 0.95 0.0265131 0.0446216
St. Benet Sherehog 1670 1740 M 1.000123 1.000414 34.0694974 34.7174821 36.0672253 33191.8 0.0286473 0.95 23.6417236 43.3454393
Chelsea Old church 1712 1842 alpha 1.000092 1.000284 0.0083989 0.0083033 0.0082201 24055.1 0.0000095 0.95 0.0056545 0.0113658
Chelsea Old church 1712 1842 beta 1.000107 1.000363 0.0422444 0.0421520 0.0421527 20068.2 0.0000343 0.95 0.0327982 0.0517568
Chelsea Old church 1712 1842 M 1.000066 1.000214 50.2412943 50.4255236 50.6944550 32126.8 0.0173728 0.95 43.9580757 56.1242381
St. Marylebone 1742 1817 alpha 1.000026 1.000095 0.0125953 0.0125006 0.0123046 29334.6 0.0000102 0.95 0.0092608 0.0160318
St. Marylebone 1742 1817 beta 1.000017 1.000034 0.0420937 0.0420895 0.0423370 23957.1 0.0000291 0.95 0.0331445 0.0508272
St. Marylebone 1742 1817 M 1.000036 1.000085 40.5179648 40.7766676 41.3760128 31991.5 0.0170220 0.95 34.3796076 46.1332104
St. Marylebone Paddington Street north 1772 1853 alpha 1.000045 1.000166 0.0099037 0.0098127 0.0096774 27403.8 0.0000087 0.95 0.0071709 0.0127837
St. Marylebone Paddington Street north 1772 1853 beta 1.000055 1.000206 0.0488613 0.0488575 0.0485839 23270.2 0.0000301 0.95 0.0398523 0.0578266
St. Marylebone Paddington Street north 1772 1853 M 1.000039 1.000116 44.6690555 44.7919466 45.0496301 37001.7 0.0116510 0.95 40.1953904 48.9817326
St. Bride’s lower churchyard 1770 1849 alpha 1.000035 1.000073 0.0061790 0.0061316 0.0059751 14779.1 0.0000071 0.95 0.0045330 0.0078754
St. Bride’s lower churchyard 1770 1849 beta 1.000155 1.000339 0.0510752 0.0510280 0.0511331 11203.6 0.0000422 0.95 0.0423814 0.0598976
St. Bride’s lower churchyard 1770 1849 M 1.000130 1.000460 53.4368072 53.4511152 53.4536777 46992.7 0.0074618 0.95 50.2090353 56.5697935
Sheen’s burial ground 1763 1854 alpha 1.000091 1.000320 0.0129642 0.0128270 0.0124596 28565.8 0.0000128 0.95 0.0089230 0.0173233
Sheen’s burial ground 1763 1854 beta 1.000171 1.000495 0.0353994 0.0353305 0.0350479 24673.6 0.0000300 0.95 0.0262620 0.0446735
Sheen’s burial ground 1763 1854 M 1.000120 1.000420 39.9956498 40.5717091 41.5741951 29050.5 0.0299067 0.95 29.5817256 49.0658033
Bow Baptist Church 1816 1854 alpha 1.000037 1.000121 0.0177742 0.0176655 0.0171967 37363.4 0.0000114 0.95 0.0135868 0.0221462
Bow Baptist Church 1816 1854 beta 1.000013 1.000063 0.0344658 0.0344556 0.0344680 30272.0 0.0000249 0.95 0.0259810 0.0429301
Bow Baptist Church 1816 1854 M 1.000031 1.000063 30.6580796 31.3283020 32.6360138 33171.9 0.0277771 0.95 20.3999444 39.3695617
St. Mary and St. Michael 1843 1853 alpha 1.000523 1.001826 0.0186478 0.0185639 0.0182508 41699.1 0.0000099 0.95 0.0148267 0.0227130
St. Mary and St. Michael 1843 1853 beta 1.000441 1.001467 0.0402140 0.0402172 0.0404972 35162.0 0.0000216 0.95 0.0322916 0.0481568
St. Mary and St. Michael 1843 1853 M 1.000616 1.001944 30.8426109 31.1889790 31.6656994 38394.2 0.0171194 0.95 24.1587401 36.9724139
St. Bride’s crypt (known age) 1740 1853 alpha 1.001301 1.004385 0.0048650 0.0048100 0.0046364 11054.4 0.0000077 0.95 0.0033513 0.0064885
St. Bride’s crypt (known age) 1740 1853 beta 1.001527 1.004999 0.0492998 0.0492831 0.0490777 10841.1 0.0000350 0.95 0.0422819 0.0564716
St. Bride’s crypt (known age) 1740 1853 M 1.000820 1.002819 59.1168993 59.1961001 59.4409448 16528.6 0.0139187 0.95 55.5069567 62.4858268
St. Bride’s crypt (estimates) 1740 1853 alpha 1.000250 1.000942 0.0050511 0.0049857 0.0049500 13935.6 0.0000077 0.95 0.0033266 0.0068431
St. Bride’s crypt (estimates) 1740 1853 beta 1.000251 1.000919 0.0461973 0.0460966 0.0460772 11655.0 0.0000408 0.95 0.0375863 0.0548062
St. Bride’s crypt (estimates) 1740 1853 M 1.000110 1.000431 60.0918241 60.1324772 60.2370171 29765.3 0.0137390 0.95 55.4315320 64.7329115
kable(wellcome_result_r, caption = "London cemeteries data, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London cemeteries data, corrected for population growth.
cemetery start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
Bermondsey Abbey 1089 1538 alpha 1.0001999 1.0007416 0.0105288 0.0104025 0.0101065 26895.4 0.0000111 0.95 0.0071225 0.0141935
Bermondsey Abbey 1089 1538 beta 1.0003786 1.0010986 0.0429176 0.0429090 0.0434181 24113.7 0.0000308 0.95 0.0335341 0.0522185
Bermondsey Abbey 1089 1538 M 1.0001327 1.0004472 44.7061829 44.9293082 45.3226906 30386.5 0.0198385 0.95 37.7940665 51.2834230
Bermondsey Abbey 1089 1538 rate 1.0000303 1.0000756 0.0039098 0.0039108 0.0039733 106914.0 0.0000076 0.95 -0.0009505 0.0088325
St. Mary Graces 1350 1540 alpha 1.0001410 1.0003568 0.0169749 0.0168588 0.0167558 33748.3 0.0000119 0.95 0.0128271 0.0213266
St. Mary Graces 1350 1540 beta 1.0000433 1.0001007 0.0372463 0.0372464 0.0370084 30177.8 0.0000242 0.95 0.0289760 0.0454249
St. Mary Graces 1350 1540 M 1.0001281 1.0002492 32.7675640 33.2209124 33.9417464 31746.8 0.0236912 0.95 24.2993787 40.4275089
St. Mary Graces 1350 1540 rate 1.0001305 1.0004837 0.0051616 0.0051627 0.0052870 100496.1 0.0000078 0.95 0.0003122 0.0100454
St. Mary Hospital, 1120-1200 1120 1200 alpha 1.0000331 1.0001286 0.0228885 0.0227897 0.0226513 43799.9 0.0000115 0.95 0.0183155 0.0276638
St. Mary Hospital, 1120-1200 1120 1200 beta 1.0000350 1.0001314 0.0379869 0.0379887 0.0379277 41935.6 0.0000186 0.95 0.0304787 0.0454167
St. Mary Hospital, 1120-1200 1120 1200 M 1.0000459 1.0001549 24.9940336 25.4195077 26.1632091 39863.2 0.0202351 0.95 16.8860536 32.3216380
St. Mary Hospital, 1120-1200 1120 1200 rate 1.0000328 1.0000475 0.0028308 0.0028305 0.0028200 115634.2 0.0000073 0.95 -0.0021173 0.0076306
St. Mary Hospital, 1200-1250 1200 1250 alpha 1.0000810 1.0003099 0.0230203 0.0229469 0.0229048 50830.0 0.0000094 0.95 0.0189207 0.0272159
St. Mary Hospital, 1200-1250 1200 1250 beta 1.0001545 1.0005234 0.0398856 0.0398998 0.0399483 51029.8 0.0000157 0.95 0.0328956 0.0468336
St. Mary Hospital, 1200-1250 1200 1250 M 1.0000928 1.0003558 25.5429589 25.8389492 26.4616904 46661.4 0.0149967 0.95 19.0144549 31.4789393
St. Mary Hospital, 1200-1250 1200 1250 rate 1.0000406 1.0000908 0.0129320 0.0129281 0.0127274 107875.9 0.0000076 0.95 0.0080676 0.0177871
St. Mary Hospital, 1250-1400 1250 1400 alpha 1.0000497 1.0001170 0.0184492 0.0184122 0.0182888 23215.0 0.0000084 0.95 0.0159587 0.0209832
St. Mary Hospital, 1250-1400 1250 1400 beta 1.0000407 1.0001310 0.0588094 0.0588085 0.0589706 23589.8 0.0000177 0.95 0.0534970 0.0641442
St. Mary Hospital, 1250-1400 1250 1400 M 1.0000497 1.0001156 31.6963826 31.7396954 31.8464384 24117.1 0.0070508 0.95 29.5007009 33.7824781
St. Mary Hospital, 1250-1400 1250 1400 rate 0.9999962 0.9999989 -0.0026207 -0.0026209 -0.0027932 56055.6 0.0000104 0.95 -0.0073601 0.0022509
St. Mary Hospital, 1400-1539 1400 1539 alpha 1.0000223 1.0000549 0.0231055 0.0230308 0.0230113 41925.6 0.0000104 0.95 0.0190097 0.0273502
St. Mary Hospital, 1400-1539 1400 1539 beta 1.0000087 1.0000259 0.0399576 0.0399616 0.0400633 39732.1 0.0000178 0.95 0.0330820 0.0469712
St. Mary Hospital, 1400-1539 1400 1539 M 1.0000141 1.0000391 25.4683995 25.7644549 26.3462367 38317.9 0.0165837 0.95 18.9737587 31.4815633
St. Mary Hospital, 1400-1539 1400 1539 rate 1.0000340 1.0000951 0.0050553 0.0050563 0.0051778 103432.2 0.0000077 0.95 0.0001496 0.0098918
New Churchyard 1569 1739 alpha 1.0001279 1.0002871 0.0211766 0.0211136 0.0212054 37764.5 0.0000100 0.95 0.0174176 0.0249711
New Churchyard 1569 1739 beta 1.0000753 1.0001933 0.0400944 0.0400933 0.0400801 35294.2 0.0000185 0.95 0.0332312 0.0468600
New Churchyard 1569 1739 M 1.0001440 1.0003447 27.7108539 27.9722139 28.4872019 35217.0 0.0160479 0.95 21.6010226 33.2292167
New Churchyard 1569 1739 rate 1.0000620 1.0001365 0.0082621 0.0082646 0.0083576 87104.3 0.0000084 0.95 0.0033814 0.0131413
St. Benet Sherehog 1670 1740 alpha 1.0001805 1.0006101 0.0132861 0.0131411 0.0129458 34008.4 0.0000119 0.95 0.0091934 0.0176933
St. Benet Sherehog 1670 1740 beta 1.0001190 1.0003512 0.0381719 0.0381737 0.0382241 31530.9 0.0000266 0.95 0.0289791 0.0474535
St. Benet Sherehog 1670 1740 M 1.0002037 1.0006791 39.3972135 39.8401136 40.1526185 34591.5 0.0241655 0.95 30.3535344 47.6481468
St. Benet Sherehog 1670 1740 rate 1.0000344 1.0000931 0.0059873 0.0059983 0.0060528 119114.7 0.0000072 0.95 0.0011010 0.0108270
Chelsea Old church 1712 1842 alpha 1.0002873 1.0010299 0.0058789 0.0057818 0.0055736 24844.5 0.0000075 0.95 0.0036917 0.0082560
Chelsea Old church 1712 1842 beta 1.0002128 1.0007988 0.0472765 0.0472197 0.0472248 21617.0 0.0000341 0.95 0.0374445 0.0571072
Chelsea Old church 1712 1842 M 1.0001776 1.0006011 56.3070206 56.3582529 56.7461356 44134.7 0.0138780 0.95 50.5873981 62.0866861
Chelsea Old church 1712 1842 rate 1.0000451 1.0001660 0.0100601 0.0100643 0.0101297 89138.8 0.0000084 0.95 0.0051571 0.0149469
St. Marylebone 1742 1817 alpha 1.0000748 1.0001372 0.0095679 0.0094649 0.0091973 30628.4 0.0000087 0.95 0.0067098 0.0125807
St. Marylebone 1742 1817 beta 1.0000415 1.0001241 0.0459357 0.0459208 0.0457528 27451.1 0.0000277 0.95 0.0370076 0.0549197
St. Marylebone 1742 1817 M 1.0000736 1.0001274 46.1751078 46.2984132 46.3570171 40003.8 0.0136968 0.95 40.7083583 51.4616051
St. Marylebone 1742 1817 rate 1.0000683 1.0002323 0.0095688 0.0095712 0.0093581 99214.5 0.0000079 0.95 0.0047434 0.0145099
St. Marylebone Paddington Street north 1772 1853 alpha 1.0000358 1.0000900 0.0065801 0.0065013 0.0064360 29127.9 0.0000066 0.95 0.0044463 0.0087891
St. Marylebone Paddington Street north 1772 1853 beta 1.0001415 1.0004460 0.0544281 0.0544209 0.0547945 26218.3 0.0000292 0.95 0.0452271 0.0637787
St. Marylebone Paddington Street north 1772 1853 M 0.9999975 1.0000085 50.9632692 50.9739902 50.9618065 49233.1 0.0098106 0.95 46.6741737 55.2372052
St. Marylebone Paddington Street north 1772 1853 rate 1.0000364 1.0001074 0.0144206 0.0144255 0.0141691 101071.9 0.0000078 0.95 0.0094983 0.0192607
St. Bride’s lower churchyard 1770 1849 alpha 1.0011697 1.0042730 0.0037341 0.0036868 0.0036269 16620.6 0.0000049 0.95 0.0025631 0.0049982
St. Bride’s lower churchyard 1770 1849 beta 1.0015090 1.0051365 0.0582705 0.0582224 0.0580684 12836.2 0.0000410 0.95 0.0491681 0.0672636
St. Bride’s lower churchyard 1770 1849 M 1.0003029 1.0011116 59.3567949 59.3049875 59.1753323 40772.1 0.0095119 0.95 55.5901301 63.1117920
St. Bride’s lower churchyard 1770 1849 rate 1.0003038 1.0011395 0.0143225 0.0143172 0.0141355 52696.3 0.0000108 0.95 0.0094154 0.0191705
Sheen’s burial ground 1763 1854 alpha 1.0001549 1.0002068 0.0081112 0.0079857 0.0076079 28990.1 0.0000095 0.95 0.0051656 0.0113978
Sheen’s burial ground 1763 1854 beta 1.0000827 1.0001417 0.0418442 0.0418050 0.0417337 27930.4 0.0000294 0.95 0.0322170 0.0514367
Sheen’s burial ground 1763 1854 M 1.0001259 1.0001599 51.3035346 51.4719153 51.7458183 37127.6 0.0196709 0.95 43.8156221 58.7122226
Sheen’s burial ground 1763 1854 rate 1.0000471 1.0000606 0.0143440 0.0143429 0.0142681 101954.9 0.0000078 0.95 0.0093921 0.0191445
Bow Baptist Church 1816 1854 alpha 1.0000751 1.0002591 0.0110080 0.0109048 0.0107115 41439.7 0.0000082 0.95 0.0078878 0.0143335
Bow Baptist Church 1816 1854 beta 1.0000831 1.0003245 0.0409501 0.0409441 0.0407475 36617.2 0.0000234 0.95 0.0322211 0.0497674
Bow Baptist Church 1816 1854 M 1.0000690 1.0002060 44.0086393 44.2046299 44.6069317 46933.1 0.0152560 0.95 37.4300374 50.3741413
Bow Baptist Church 1816 1854 rate 1.0000216 1.0000239 0.0174851 0.0174851 0.0173758 106259.5 0.0000076 0.95 0.0125967 0.0223740
St. Mary and St. Michael 1843 1853 alpha 1.0001563 1.0005720 0.0122807 0.0121938 0.0120196 46093.7 0.0000074 0.95 0.0092409 0.0154457
St. Mary and St. Michael 1843 1853 beta 1.0002253 1.0007624 0.0459562 0.0459699 0.0456100 42613.3 0.0000202 0.95 0.0378149 0.0541866
St. Mary and St. Michael 1843 1853 M 1.0001425 1.0005089 40.6794124 40.8054593 41.3726101 51800.7 0.0109648 0.95 35.7481079 45.5245164
St. Mary and St. Michael 1843 1853 rate 1.0000407 1.0001181 0.0176425 0.0176439 0.0178219 111336.5 0.0000075 0.95 0.0128415 0.0226355
St. Bride’s crypt (known age) 1740 1853 alpha 11.3187848 26.7160198 0.0062628 0.0058303 0.0034420 1.5 0.0018915 0.95 0.0031442 0.0102527
St. Bride’s crypt (known age) 1740 1853 beta 11.7161168 22.9647008 0.0510415 0.0510591 0.0509381 1.4 0.0034864 0.95 0.0443241 0.0572525
St. Bride’s crypt (known age) 1740 1853 M 11.7488400 23.5976438 53.9513110 54.4984270 54.3621152 1.4 4.7419679 0.95 44.8901900 62.3280593
St. Bride’s crypt (known age) 1740 1853 rate 1.0001302 1.0004858 -0.9898864 -0.9898864 -0.9898825 68206.5 0.0000004 0.95 -0.9900793 -0.9896890
St. Bride’s crypt (estimates) 1740 1853 alpha 1.0010883 1.0036469 0.8089951 0.8096464 0.8091857 3141.3 0.0003460 0.95 0.7708209 0.8467743
St. Bride’s crypt (estimates) 1740 1853 beta 1.0011031 1.0035351 0.0049692 0.0049308 0.0048867 3152.0 0.0000121 0.95 0.0036820 0.0063247
St. Bride’s crypt (estimates) 1740 1853 M 1.0008190 1.0029237 -1038.5780551 -1022.5151667 -1000.6858905 3228.3 3.1452459 0.95 -1405.8300586 -716.0579775
St. Bride’s crypt (estimates) 1740 1853 rate 1.0000235 1.0000707 -0.9873975 -0.9873961 -0.9874078 123992.2 0.0000071 0.95 -0.9922468 -0.9824618

5 Supplements

The chapter ‘Supporting informations’ provides details about the London cemeteries included in the study.

5.1 The Coale & Demeny life tables

Calculation of the lowest \(\beta\)-value for any of the Coale & Demeny life tables (Coale/Demeny (1983)) which is 0.0391 (the female table “West”, level 1).

source("./chapter_supplement/coale_demeny_life_tables_gompertz.R")
min(gompertz_df$Gompertz_shape)
## [1] 0.03913138

5.2 Simulations

Simulations for evaluation of algorithms for retrieving Gompertz parameters. The file “./chapter_supplement/simulations_run.R” provides various tests and plots from the evaluation process. The validity of the algorithms is tested via root mean square error (RMSE) of between expected and estimated values for Gompertz \(\beta\).

5.2.1 Known age-at-death

Figure S1: Comparing expected and estimated Gompertz \(\beta\)-values by different algorithms with known age-at-death (n = 1,000).

source("./chapter_supplement/simulations_run.R")
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
gridExtra::grid.arrange(grobs = plot_list_shapes, ncol = 3)

Figure S2: Difference between expected and estimated Gompertz \(\beta\)-values by different algorithms with known age-at-death (n = 1,000).

source("./chapter_supplement/simulations_run.R")
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
gridExtra::grid.arrange(grobs = plot_list_diff, ncol = 3)

Table S1: Root mean square errors (RMSE) for different formulas for fitting known age-at-death, ordered ascendingly.

# table of RMSEs
kable(rmse_result[order(rmse_result$RMSE) ,], caption = "Evaluation of algorithms via RMSE.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position") 
Evaluation of algorithms via RMSE.
method RMSE NAs
11 Bayes (5y-cat) 0.0041953 0
10 Bayes 0.0042255 0
4 survival 0.0042981 0
7 MLE 0.0043000 0
12 Bayes (10y-cat) 0.0043487 0
8 MLE (5y-cat) 0.0043686 0
9 MLE (10y-cat) 0.0045265 0
5 survival (5y-cat) 0.0046064 0
1 OLS 0.0049051 519
3 WNLS 0.0053132 16
2 WOLS 0.0057136 0
6 survival (10y-cat) 0.0065228 0
13 Bayes poisson 0.0106965 0

Figure S3: Comparing expected and estimated Gompertz \(\beta\)-values by different algorithms with estimated age-at-death (n = 1,000).

source("./chapter_supplement/simulations_run.R")
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
gridExtra::grid.arrange(grobs = plot_list_estim_shapes, ncol = 2)

Table S2: Root mean square errors (RMSE) for different formulas for fitting estimated age-at-death, ordered ascendingly.

# table of RMSEs
kable(rmse_estim_result[order(rmse_estim_result$RMSE) ,], caption = "Evaluation of algorithms via RMSE for estimated age-at-death.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position") 
Evaluation of algorithms via RMSE for estimated age-at-death.
method RMSE NAs
8 MLE_wo_OL 0.0128521 18
6 Bayes (cat) 0.0137203 0
1 OLS 0.0237398 95
3 WNLS 0.0260833 9
2 WOLS 0.0276202 0
5 MLE (cat) 0.0302704 0
7 Bayes poisson 0.0599111 0
4 survival (cat) 0.1454623 0

Figure S4: Detailed plot for the Bayesian model of expected Gompertz \(\beta\)-values (left) and sample size (right) vs. difference of expected/estimated Gompertz \(\beta\)-values.

#source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_bayes_diff, ncol = 2)

5.2.2 Stability of means

Show that means are stable in Bayesian modelling, regardless of the number of MCMC-steps.

source("./chapter_supplement/bayes_complete.R") # can take a few minutes
kable (bayes_complete, caption = paste0("Bayesian model with simulated dataset and different number of steps. n = ", 
                              n, ", Gompertz beta = ", round(beta, 4), ".", sep = "")) %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Bayesian model with simulated dataset and different number of steps. n = 500, Gompertz beta = 0.05.
mode thinning steps parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
known_age 1 10000 a 1.003210 1.006108 0.0028582 0.0028441 0.0027725 462.7 0.0000154 0.95 0.0022403 0.0035193
known_age 1 10000 b 1.001893 1.003920 0.0480363 0.0480265 0.0481745 488.6 0.0000947 0.95 0.0440097 0.0520917
known_age 1 10000 M 1.001259 1.003216 73.8375371 73.8501409 73.6934420 930.5 0.0357533 0.95 71.6915433 75.9608132
known_age 20 100000 a 1.000011 1.000109 0.0028495 0.0028327 0.0027934 71982.2 0.0000013 0.95 0.0022163 0.0035260
known_age 20 100000 b 1.000005 1.000090 0.0480993 0.0480962 0.0483082 71181.0 0.0000080 0.95 0.0438344 0.0521777
known_age 20 100000 M 1.000000 1.000078 73.8543153 73.8768307 73.9884330 84071.3 0.0037849 0.95 71.6339091 75.9294081
estimation 1 10000 a 1.007384 1.023678 0.0028312 0.0028026 0.0027942 167.5 0.0000382 0.95 0.0019049 0.0038193
estimation 1 10000 b 1.011691 1.038693 0.0510970 0.0508290 0.0503803 86.5 0.0005942 0.95 0.0404465 0.0624583
estimation 1 10000 M 1.005548 1.017117 71.9242579 71.9119671 72.0531786 392.2 0.1119194 0.95 67.6950056 76.3291669
estimation 20 100000 a 1.000247 1.000941 0.0027769 0.0027509 0.0027034 29177.9 0.0000026 0.95 0.0019290 0.0036726
estimation 20 100000 b 1.000354 1.001342 0.0516959 0.0514776 0.0502964 20843.0 0.0000356 0.95 0.0421542 0.0619696
estimation 20 100000 M 1.000091 1.000334 71.8362699 71.7754410 71.6155191 45976.8 0.0102799 0.95 67.6297829 76.2104655

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  1. Institute for Pre- and Proto History - Kiel University ↩︎

  2. Institute of Clinical Molecular Biology - Kiel University, ↩︎

  3. Institute for Pre- and Proto History - Kiel University, ↩︎